Low Energy Event Reconstruction with Super-Kamiokande
Vertex Fit
The electrons produced by elastic scattering of
solar 8B neutrinos are fairly low in energy
(below 20 MeV) so they do not travel far in water
(less than a few centimeters). This justifies the
use of a point (vertex) fitter of the analysis.
Fitting strategies
Standard Low Energy Vertex fit
Currently, the fitting starts by selecting hit photomultiplier tubes
using their absolute timing coincidence.
Then, a vertex goodness criterion is defined for those selected
photomultiplier tubes. This goodness is a function of space
and ranges from 0 to 1. It roughly corresponds to the ratio
of in-time (after time-of-flight subtraction from a given vertex)
hits over all selected hits.
A grid search method is used to find the position with the largest
goodness value. This position is chosen as the reconstructed vertex.
The grid is Cartesian; evenly spaced in the coordinates x, y and z.
Mr. Clean
The idea of the Mr. Clean algorithm is to
first `clean up' the hit
photomultiplier tubes by only admitting those tubes to the fit,
that have at least one spatial and one temporal `neighbor'. A spatial
neighbor must be located closer than 700 cm, a temporal neighbor
must be in-time with a precision of 35 nsec.
Cluster fit
This algorithm changes the hit selection of the
standard algorithm (timing coincidence).
It also changes the grid type from Cartesian to
cylindrical and interpolates the maximum goodness from the
grid goodness values.
The new hit selection looks at pairs of hit photomultiplier tubes
and checks them for consistency with a common vertex using the
triangle inequality: delta(x)+t must be smaller than delta(t)+t or
delta(x) smaller than delta(t).
It proceeds by forming
sets of hits where all pair subsets are consistent
with a common vertex. Finally, all sets with the largest number of
hits are merged.
The algorithm also uses a Mr. Clean pre-selection (where the
spatial criterion is loosened to 1250 cm).
LINAC calibration data was used to test various vertex fit algorithms.
The algorithms perform very similar in core resolution but differ in
the mis-fit tails (events reconstructed further than 3m away from the
true vertex.) Four algorithms were tested: standard algorithm (JLE),
Extinction (similar to cluster fit) cluster fit (without Mr. Clean)
and clean cluster (with Mr. Clean)
The error bar shown is the spread arising from the position dependence.
The vertical axis measures the fraction of good fits (closer than 3m),
the horizontal axis the LINAC energy.
Direction Fit
After the vertex of a low energy event is
reconstructed, the direction fit selects
hit photomultiplier tubes that
recorded a hit time within
50 nsec of the expected time. A maximum
likelihood fit reconstructs the
direction. Multiple Coulomb scattering renders
this task difficult. Since the directional correlation
of Solar neutrino event candidates with the expected
position of the sun is used to separate the Solar
signal from residual background, a good directional
resolution is highly important for
the analysis.
The Ariadne algorithm uses a different approach.
The maximum likelihood fit is replaced by a
more transparent, direct fitting approach. Ariadne
attempts to separate the hits originating from the
original direction of the electron (assuming, that
it produced the largest number of photons) from the hits after
the first scattering took place, thereby improving
the directional resolution.
It looks first at pairs of hits which lead to zero,
one, or two direction solutions.
Ariadne then
adds to each solution the vectors of all other solutions
that are consistent with it (the cosine of the angle
theta between them must be bigger than 0.9).
The longest resulting vector is chosen and the ratio of
its length and the largest possible
length (if all solutions would perfectly line up) reflects
the goodness of the fit direction.
The Ariadne algorithm improves the angular
resolution. However, it has a larger bias than the maximum
likelihood fit to reconstruct along the Z axis due to
the cylindrical shape of Super-Kamiokande.